Question: Simplify the following expression: $ q = \dfrac{k + 1}{-9} - 9 $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the second expression by $\dfrac{-9}{-9}$ $ \dfrac{9}{1} \times \dfrac{-9}{-9} = \dfrac{-81}{-9} $ Therefore $ q = \dfrac{k + 1}{-9} - \dfrac{-81}{-9} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{k + 1 + 81 }{-9} $ Distribute the negative sign: $q = \dfrac{k + 1 + 81}{-9}$ $q = \dfrac{k + 82}{-9}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{-k - 82}{9}$